[1] Arjovsky M, Chintala S, Botou L. Wasserstein GAN[J]. arXiv:1701.07875v3, 2017, 1-26.
[2] Rubner Y, Tomasi C, Guibas L J. The earth mover's distance as ametric for image retrieval[J]. International Journal ofComputer Vision, 2000, 40(2):99-121.
[3] Villani C. Optimal Transport:Old and New[M]. Berlin:Springer-Verlag, 2008.
[4] Santamorogio F. Optimal Transport for Applied Mathematics[M].Birkäuser, Cham, 2015.
[5] Monge G. Mémoire sur la Théorie des Déblais et des Remblais[M]. Paris:De ĺImprimerie Royale, 1781.
[6] Kantorovich L. On translation of mass(in Russian)[J]. Dokl. ANSSSR, 1942, 37:199-201.
[7] Kolouri S, Park S R, Thorpe M, et al. Optimal mass transport:Signalprocessing and machine-learning applications[J]. IEEE SignalProcessing Magazine, 2017, 34(4):43-59.
[8] Brenier Y. Polar factorization and monotone rearrangement of vector-valued functions[J].Communications on Pure and Applied Mathematics, 1991, 44(4):375-417.
[9] Gangbo W, McCann R J. The geometry of optimal transportation[J].Acta Mathematica, 1996, 177(2):113-161.
[10] Agueh M, Carlier G. Barycenters in the Wasserstein space[J]. SIAM Journal on Mathematical Analysis, 2011, 43(2):904-924.
[11] Ferradans S, Papadakis N, Rabin J, et al. Regularized discreteoptimal transport[J]. SIAM Journal on Imaging Sciences, 2013,7(3):428-439.
[12] Kuhn H W. The Hungarian method for the assignment problem[J]. Naval Research Logistics Quarterly, 1955, 2(1-2):83-97.
[13] Bertsekas D P. The auction algorithm:A distributed relaxationmethod for the assignment problem[J]. Annals of OperationsResearch, 1988, 14(1):105-123.
[14] Rabin J, Ferradans S, Papadakis N. Adaptive color transfer withrelaxed optimal transport[C]//IEEE international Conferenceon Image Processing, Paris, France, Oct 2014, 4852-4856.
[15] Louet J, Santambrogio F. A sharp inequality for transport maps in W1,p(R) via approximation[J]. AppliedMathematics Letters, 2012, 25(3):648-653.
[16] Papadakis N. Optimal Transport for Image Processing[M].Signal and Image Processing, Université de Bordeaux, 2015.
[17] Gilboa G, Osher S. Nonlocal linear image regularization andsupervised segmentation[J]. SIAM Multiscale Modeling andSimulation, 2007, 6(2):595-630.
[18] Cuturi M. Sinkhorn distances:Lightspeed computation of optimaltransport[C]//Advances in Neural Information ProcessingSystems, 2013, 2292-2300.
[19] Knight P. The sinkhorn-knopp algorithm:Convergence and applications[J]. SIAM Journal on Matrix Analysis and Applications, 2008,30(1):261-275.
[20] Courty N, Flamary R, Tuia D. Domain adaptation with regularizedoptimal transport[C]//Joint European Conference on MachineLearning and Knowledge Discovery in Databases.Springer, Berlin, Heidelberg, 2014:274-289.
[21] Courty N, Flamary R, Tuia D, et al. Optimal transport for domainadaptation[J]. IEEE Transactions on Pattern Analysis andMachine Intelligence, 2017, 39(9):1853-1865.
[22] Nesterov Y E, Nemirovsky A S. Interior Point Polynomial Methodsin Convex Programming:Theory and Algorithms[M].SIAM Publishing, 1993.
[23] 袁亚湘, 孙文瑜. 最优化理论与方法[M].北京:科学出版社, 1997.
[24] Ahuja R K, Magnanti T, Orlin J. Network Flows:Theory,Algorithms, and Applications[M]. Prentice Hall, Upper SaddleRiver, 1993.
[25] Zaslavskiy M, Bach F, Vert J P. A path following algorithm for thegraph matching problem[J]. IEEE Transactions on PatternAnalysis and Machine Intelligence, 2009, 31(12):2227-2242.
[26] Shirdhonkar S, Jacobs D W. Approximate earth mover's distance inlinear time[C]//2008 IEEE Conference on Computer Vision andPattern Recognition, IEEE, 2008, 1-8.
[27] Rabin J, Peyré G, Delon J, et al. Wasserstein barycenter and itsapplication to texture mixing[C]//International Conference onScale Space and Variational Methods in Computer Vision,Berlin:Springer, 2011, 435-446.
[28] Sinkhorn R. Diagonal equivalence to matrices with prescribed row andcolumn sums[J]. The American Mathematical Monthly, 1967,74(4):402-405.
[29] Solomon J, De Goes F, Peyré G, et al.Convolutional wasserstein distances:Efficient optimal transportation on geometric domains[J].ACM Transactions on Graphics, 2015, 34(4):66:1-66:11
[30] Zhao Q, Yang Z, Tao H. Differential earth mover's distance with itsapplications to visual tracking[J]. IEEE Transactions onPattern Analysis and Machine Intelligence, 2010, 32(2):274-287.
[31] Rubner Y, Tomasi C, Guibas L J. A metric for distributions withapplications to image databases[C]//Sixth InternationalConference on Computer Vision (IEEE Cat. No. 98CH36271), IEEE, 1998, 59-66.
[32] Ling H, Okada K. An efficient earth mover's distance algorithm forrobust histogram comparison[J]. IEEE Transactions on PatternAnalysis and Machine Intelligence, 2007, 29(5):840-853.
[33] Pele O, Werman M. Fast and robust earth mover's distances[C]//2009 IEEE 12th International Conference on Computer Vision, IEEE,2009, 460-467.
[34] Tahri O, Usman M, Demonceaux C, et al. Fast earth mover's distancecomputation for catadioptric image sequences[C]//2016 IEEEInternational Conference on Image Processing (ICIP), IEEE, 2016,2485-2489.
[35] Thibault A, Chizat L, Dossal C, et al. Overrelaxed sinkhorn-knoppalgorithm for regularized optimal transport[J]. arXiv preprintarXiv:1711.01851, 2017, 1-10.
[36] Dvurechensky P, Gasnikov A, Kroshnin A. Computational optimaltransport:Complexity by accelerated gradient descent is better thanby Sinkhorn's algorithm[J]. arXiv preprint arXiv:1802.04367, 2018, 1-25.
[37] Haker S, Zhu L, Tannenbaum A, et al.Optimal mass transport for registration and warping[J].International Journal of Computer Vision, 2004, 60(3):225-240.
[38] Angenent S, Haker S, Tannenbaum A. Minimizing flows for theMonge-Kantorovich problem[J]. SIAM Journal on MathematicalAnalysis, 2003, 35(1):61-97.
[39] Benamou J D, Froese B D, Oberman A M.Numerical solution of the optimal transportation problem using the Monge-Ampére equation[J].Journal of Computational Physics, 2014, 260:107-126.
[40] Gu X,Luo F,Sun J, et al. Variational principles for Minkowski typeproblems, discrete optimal transport and discrete Monge-Ampereequations[J]. Asian Journal of Mathematics, 2016, 20(2):383-398.
[41] Su Z, Sun J, Gu X, et al. Optimal mass transport for geometricmodeling based on variational principles in convex geometry[J].Engineering with Computers, 2014, 30(4):475-486.
[42] Liu J, Froese B D, Oberman A M, et al. A multigrid scheme for 3DMonge-Ampére equations[J]. International Journal ofComputer Mathematics, 2017, 94(9):1850-1866.
[43] Bing S, Gang H. Order-preserving optimal transport for distancesbetween sequences[J]. IEEE Transactions on Pattern Analysisand Machine Intelligence, 2018:1-14. DOI:10.1109/tpami.2018.2870154.
[44] Li P, Wang Q, Zhang L. A novel earth mover's distance methodologyfor image matching with gaussian mixture models[C]//Proceedings of the IEEE International Conference on ComputerVision, 2013, 1689-1696.
[45] Bonneel N, Peyré G, Cuturi M. Wasserstein barycentriccoordinates:histogram regression using optimal transport[J]. ACM Transactions on Graphics, 2016, 35(4):71:1-71:10.
[46] Pitie F, Kokaram A C, Dahyot R. N-dimensional probability densityfunction transfer and its application to color transfer[C]//Tenth IEEE International Conference on Computer Vision (ICCV'05),IEEE, 2005, Volume 1.2:1434-1439.
[47] Bonneel N, Rabin J, Peyré G, et al. Sliced and radon wassersteinbarycenters of measures[J]. Journal of Mathematical Imagingand Vision, 2015, 51(1):22-45.
[48] Rehman T ur, Haber E, Pryor G, et al. 3D nonrigid registration viaoptimal mass transport on the GPU[J]. Medical Image Analysis,2009, 13(6):931-940.
[49] Museyko O, Stiglmayr M, Klamroth K, et al. On the application of theMonge-Kantorovich problem to image registration[J]. SIAMJournal on Imaging Sciences, 2009, 2(4):1068-1097.
[50] Papież B W, Brady M, Schnabel J A. Mass transportation fordeformable image registration with application to Lung CT. Molecular Imaging, Reconstruction and Analysis of Moving BodyOrgans, and Stroke Imaging and Treatment, Springer, Cham, 2017, 66-74.
[51] Xu D, Yan S, Luo J. Face recognition using spatially constrainedearth mover's distance[J]. IEEE Transactions on ImageProcessing, 2008, 17(11):2256-2260.
[52] Schmitz M A, Heitz M, Bonneel N, et al. Wasserstein dictionarylearning:Optimal transport-based unsupervised nonlinear dictionarylearning[J]. SIAM Journal on Imaging Sciences, 2018,11(1):643-678.
[53] Wang F, Guibas L J. Supervised earth mover's distance learning andits computer vision applications[C]//European Conference onComputer Vision, Berlin:Springer, 2012, 442-455.
[54] Peyré G, Fadili J, Rabin J. Wasserstein active contours[C]//201219th IEEE International Conference on Image Processing,IEEE, 2012, 2541-2544.
[55] Mendoza C, Pérez-Carrasco J A, Sáez A, et al. Linearizedmultidimensional earth-mover's-distance gradient flows[J]. IEEE Transactions on Image Processing, 2013, 22(12):5322-5335.
[56] Papadakis N, Rabin J.Convex histogram-based joint image segmentation with regularized optimal transport cost[J].Journal of Mathematical Imaging and Vision, 2017, 59(2):161-186.
[57] Rabin J, Papadakis N. Convex color image segmentation with optimaltransport distances[C]//International Conference on ScaleSpace and Variational Methods in Computer Vision, Springer, Cham,2015, 256-269.
[58] Ni K, Bresson X, Chan T F, et al. Local histogram based segmentationusing the wasserstein distance[J]. International Journal ofComputer Vision, 2009, 84(1):97-111.
[59] Swoboda P, Schnörr C. Variational image segmentation andcosegmentation with the wasserstein distance. InternationalWorkshop on Energy Minimization Methods in Computer Vision andPattern Recognition, Berlin:Springer, 2013, 321-334.
[60] Yildizoglu R, Aujol J F, Papadakis N. A convex formulation forglobal histogram based binary segmentation[C]//InternationalConference on Energy Minimization Methods in Computer Vision andPattern Recognition, 2013, 335-349.
[61] Cuturi M, Peyré G. A smoothed dual approach for variationalWasserstein problems[J]. SIAM Journal on Imaging Sciences,2016, 9(1):320-343.